EXCUSE US!    We're working on Navigation!

Elevator Speed An elevator consisting of cables, pulleys, and an electric motor (8 kilowatts) steadily lifts a load of 1000 kilograms. A sketch of the elevator is shown. Use the Energy Equation for a body to calculate the theoretical maximum rate of ascent of the elevator.

♦  This elevator is not a "body," it is an extended body. We take the elevator to be a mass equal to that of the elevator and located at the center of mass of the elevator. If there is no rotation, the energy equation for a body will apply.

The elevator (modeled as an extended body) is our system. The "arrow" beside work-dot, pointing into the system, indicates the chosen sign convention that energy that passes to the system as work is considered positive.

The event is described by the rate form of the energy equation.

Components of energy and work of the event are made explicit as:

Next write the kinetic energy in terms of the steady vertical speed, v_z, also write the potential in terms of increasing elevation, z.

Differentiation of the kinetic energy is zero because the speed is constant. Differentiation of the potential energy yields the theoretical maximum unward velocity.

The term, work-dot is the rate at which energy arrives to the elevator. Since we seek the greatest possible upward speed, we have assume the entire power of the motor (8kW) is delivered as work; that none of it is lost to friction. Numbers applied to the equation provide our answer.

Actual events involve friction which is difficult to calculate. Commonly, first calculations assume no friction. The resulting answer is theoretical and rosey.